There exists circular trap in Circular Viterbi Algorithm (CVA) and deficiencies in CVA-based decoding algorithms of Tail-Biting Convolutional Codes (TBCC). A high efficient decoding algorithm is proposed for TBCC. The checking rule for circular trap in the new algorithm is that comparing whether the two maximum likelihood paths obtained from two different iterations are identical to each other, if they are identical, the CVA should be terminated. Meanwhile, when there no trap happens, a new adaptive stopping rule for CVA is proposed which is based on comparing the maximum likelihood path with the best maximum likelihood tail-biting path. Furthermore, the path used as the measurements in the checking rule and in the stopping rule is replaced by its net path metric to reduce the complexity of decoder. The results of experiments show that the new algorithm improves the decoding efficiency and reduces the decoder complexity.